Forthcoming events in this series
Algebraic theories, locally presentable categories and their application to type theories. The seminar will take place in Lecture Theatre A of the Department of Computer Science.
The seminar will take place in Lecture Theatre A, Department of Computer Science.
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Contextuality and non-locality are features of quantum mechanics which stand in sharp contrast to the realistic picture underlying classical physics. We shall describe a unified geometric perspective on these notions in terms of *obstructions to the existence of global sections*. This allows general results and structural notions to be uncovered, with quantum mechanics appearing as a special case. The natural language to use here is that of sheaves and presheaves; and cohomological obstructions can be defined which witness contextuality in a number of salient examples.
This is joint work with Adam Brandenburger
http://iopscience.iop.org/1367-2630/13/11/113036/
http://arxiv.org/abs/1102.0264
and Shane Mansfield and Rui Soares Barbosa
http://arxiv.org/abs/1111.3620
Introductory talk on topological quantum field theories (TQFTs) and the cobordism hypothesis, focusing on the conceptual issues involved.
The lecture will take place this Friday at 11am in Lecture Theatre A of the Department of Computer Science
We will demonstrate the following. Category theory, usually conceived as some very abstract form of metamathematics, is present everywhere around us. Explicitly, we show how it provides a kindergarten version of quantum theory, an how it will help Google to understand sentences rather than words.
Some references are:
-[light] BC (2010) "Quantum picturalism". Contemporary Physics 51, 59-83. arXiv:0908.1787
-[a bit heavier] BC and Ross Duncan (2011) "Interacting quantum observables: categorical algebra and diagrammatics". New Journal of Physics 13, 043016. arXiv:0906.4725
-[light] New Scientist (8 December 2010) "Quantum links let computers understand language". www.cs.ox.ac.uk/people/bob.coecke/NewScientist.pdf
-[a bit heavier] BC, Mehrnoosh Sadrzadeh and Stephen Clark (2011) "Mathematical foundations for a compositional distributional model of meaning". Linguistic Analysis - Lambek Festschrift. arXiv:1003.439
This meeting will mark the 80th birthday of Sir Roger Penrose. Twistor theory is one of his most remarkable discoveries and continues to have applications across pure mathematics and mathematical physics. This meeting will focus on some recent developments with speakers both on geometry and physics.
Speakers:
Registration will start at 1.30pm on the 21st with the first lecture at 2.15pm. The meeting will finish by 4.30pm on the 22nd. See the programme for more details.
There will be a reception at 6.30pm on the 21st July (Wadham College) followed by dinner at 7.15 in Wadham College.
We review the relation between the geometry of Kleinian singularities and Dynkin diagrams of types ADE, recalling in particular the construction of a braid group action of type A, D, or E on the derived category of coherent sheaves on the minimal resolution of a Kleinian singularity. By work of Seidel-Thomas, this action was known to be faithful in type A. We extend this faithfulness result to types ADE, which provides the missing ingredient for completing Bridgeland's description of spaces of stability conditions for certain triangulated categories associated to Kleinian singularities. Our main tool is the Garside normal form for braid group elements. This project is joint work with Hugh Thomas from the University of New Brunswick.